In a large clinical trial, 391,834 children were randomly assigned to two groups. The treatment group consisted of 197, 193 children given a vaccine for a certain disease, and 39 of thos children developed the disease. The other 194,641 children were given a placebo, and 149 of those children developed the disease. Consider the vaccine treatment group to be the firs sample. Identify the values of n, , p,, 9,, n2, P2, 92, p, and q. (Type an integer or a decimal rounded to eight decimal places as needed.) q, = 0.99980222 (Type an integer or a decimal rounded to eight decimal places as needed.) n, = 194641 =ロ (Type an integer or a decimal rounded to eight decimal places as needed.) (Type an integer or a decimal rounded to eight decimal places as needed.) p=口 (Type an integer or a decimal rounded to eight decimal places as needed.) (Type an integer or a decimal rounded to eight decimal nin

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### Clinical Trial Analysis

In a large clinical trial, 391,834 children were randomly assigned to two groups. The treatment group consisted of 197,193 children given a vaccine for a certain disease, and 39 of those children developed the disease. The other 194,641 children were given a placebo, and 149 of those children developed the disease. Consider the vaccine treatment group to be the first sample. 

#### Calculation of Values

- **\( n_1 \)**
  - Total number of children in the treatment group.
  - **Value:** 197,193
  
- **\( \hat{p}_1 \)**
  - Proportion of children in the treatment group who developed the disease.
  - Calculation: \( \hat{p}_1 = \frac{39}{197193} \)
  - **Value:** (Needs to be calculated)
  
- **\( \hat{q}_1 \)**
  - Proportion of children in the treatment group who did not develop the disease.
  - Calculation: \( \hat{q}_1 = 1 - \hat{p}_1 \)
  - **Value:** 0.99980222

- **\( n_2 \)**
  - Total number of children in the placebo group.
  - **Value:** 194,641
  
- **\( \hat{p}_2 \)**
  - Proportion of children in the placebo group who developed the disease.
  - Calculation: \( \hat{p}_2 = \frac{149}{194641} \)
  - **Value:** (Needs to be calculated)
  
- **\( \hat{q}_2 \)**
  - Proportion of children in the placebo group who did not develop the disease.
  - Calculation: \( \hat{q}_2 = 1 - \hat{p}_2 \)
  - **Value:** (Needs to be calculated)

- **\( \hat{p} \)**
  - Combined proportion of children who developed the disease in both groups.
  - Calculation depends on the combined data from both groups.
  - **Value:** (Needs to be calculated)
  
- **\( \hat{q} \)**
  - Combined proportion of children who did not develop the disease in both groups.
  - Calculation: \( \hat{q} = 1 - \hat{p} \)
  - **Value
Transcribed Image Text:### Clinical Trial Analysis In a large clinical trial, 391,834 children were randomly assigned to two groups. The treatment group consisted of 197,193 children given a vaccine for a certain disease, and 39 of those children developed the disease. The other 194,641 children were given a placebo, and 149 of those children developed the disease. Consider the vaccine treatment group to be the first sample. #### Calculation of Values - **\( n_1 \)** - Total number of children in the treatment group. - **Value:** 197,193 - **\( \hat{p}_1 \)** - Proportion of children in the treatment group who developed the disease. - Calculation: \( \hat{p}_1 = \frac{39}{197193} \) - **Value:** (Needs to be calculated) - **\( \hat{q}_1 \)** - Proportion of children in the treatment group who did not develop the disease. - Calculation: \( \hat{q}_1 = 1 - \hat{p}_1 \) - **Value:** 0.99980222 - **\( n_2 \)** - Total number of children in the placebo group. - **Value:** 194,641 - **\( \hat{p}_2 \)** - Proportion of children in the placebo group who developed the disease. - Calculation: \( \hat{p}_2 = \frac{149}{194641} \) - **Value:** (Needs to be calculated) - **\( \hat{q}_2 \)** - Proportion of children in the placebo group who did not develop the disease. - Calculation: \( \hat{q}_2 = 1 - \hat{p}_2 \) - **Value:** (Needs to be calculated) - **\( \hat{p} \)** - Combined proportion of children who developed the disease in both groups. - Calculation depends on the combined data from both groups. - **Value:** (Needs to be calculated) - **\( \hat{q} \)** - Combined proportion of children who did not develop the disease in both groups. - Calculation: \( \hat{q} = 1 - \hat{p} \) - **Value
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